Asynchronous bank of filters for sparse signal decomposition

Asynchronous signal processing addresses the need for analog devices that provide efficient representation and reconstruction of data at a low-power consumption. In this paper we propose an asynchronous filter-bank decomposer for sparse signals commonly found in biomedical applications. It is based on a modified version of the asynchronous sigma delta modulator (ASDM), a non-linear feedback system that maps the amplitude of a bounded signal into a binary signal. Signal reconstruction requires the solution of an integral equation that depends on the zero-crossing times of the ASDM output. Letting the input be the derivative of the signal, the integral equation is reduced to a first-order difference equation of which the input is a function of the zero-crossing times and a scale parameter of the ASDM. Using a bank of filters to determine the corresponding scale parameters we obtain a decomposer that samples non-uniformly and that has a recursive reconstruction. Thus the range of frequencies is set by the bank of filters and the width of local windows is set by the characteristics of the derivative of the signal at those frequencies. To illustrate the procedure we consider actual signals.